Based on the principle of virtual work,the Lagrangian function of the plane incompressible Stokes flow was established from the balance equations and the force boundary conditions.The dual variables and the Hamiltonian function were obtained by the Legendre transformation so that the problem was promoted to symplectic geometrical space under the Hamiltonian system.Furthermore,based on the properties of adjoint symplectic orthonormalization relationship of symplectic mathematics, the direct solution was used to find the eigenvalues and their respective eigenfunction vectors of the Hamiltonian operator matrix.The results of Stokes flow problems in a solidwalled cavity where flow was driven by the motion of either one of its horizontal bounding walls were presented and compared with other model results, which demonstrated the effectiveness of the proposed method.